‌y=x3−3x2−8x−4 ‌y=3x2+7x+4 ∵ Curves touch each other. ‌∴‌‌x3−3x2−8x−4=3x2+7x+4 ‌⇒‌‌x3−6x2−15x−8=0 On putting x=−1 ‌ LHS ‌‌=−1−6+15−8 ‌=−15+15=0= RHS On putting x=−1 in any curve equation, y=−1−3+8−4=0 ∴(−1,0) is the intersection point. Equation of tangent, y−y1=m(x−x1) .......(i) y‌=x3−3x2−8x−4 y′‌=3x2−6x−8 y′|(1−1,0)‌=3+6−8=1⇒m=1 Put the values into Eq. (i), ‌y−0=1(x+1) ⇒y=x+1 ⇒x−y+1=0